In orthodontics, to correct malocclusions, it is a standard procedure to attach individual teeth to a flexible component called an archwire. These are generally of a simple curved shape as illustrated in the FIGS. 1A and 1B. Commercially available archwires are formed of stainless steel or nickel titanium (e.g., Nitinol, aka TiNi or NiTi). Shape memory alloys (SMAs) such as Nitinol are particularly attractive for use as archwires because this material has “super-elastic” properties above characteristic temperatures, in addition to shape memory mechanics upon heating past those temperatures. These characteristic properties arise by virtue of the martensitic transformation that such materials undergo. Unlike strain with traditional dislocations, martensitic transformations (e.g., transformations from an austenite to a martensite configuration) operate by rearrangement of atoms along twin planes in the crystal to accommodate the stress inherently upon the alloy. The end result is completely new crystal structure (martensite) or phase.
Nickel titanium alloys used in orthodontics take full advantage of the superelasticity enabled by this phase change, often accommodating up to 6% full recovery. However, there is significant room for improvement with regard to these materials. For example, severe malocclusions present major force, sliding and super-elastic expectations upon archwires. Additionally, nickel titanium alloy wires express a large stress hysteresis upon straining after the initial elastic properties are consumed. Clinically, this means: 1) forces can often exceed levels of patient comfort; 2) resistance to sliding in brackets is dominated by binding forces between the bracket/wire; and 3) wires take a permanent set or exhibit incomplete recovery upon high straining. Nickel titanium alloys may also exhibit full strain recovery without adequate force upon unloading to efficiently move teeth due to hysteresis growth upon high strain. This graphically manifests as a low tapering unloading curve which may or may not return to zero strain. These mechanical variances often occur from inconsistent annealing or cold working.
When used for orthodontic treatment, archwires are progressed sequentially thru a bracket system ligated to a dental arch. This requires a wire change whenever the size and/or cross sectional form need adjustment. Cases generally begin with small round (e.g. 0.014″) wires and complete with large rectangular (e.g. 0.021×0.025″) wires (see, e.g., Table 1). Early stage wires are typically round shape memory alloys with superelastic properties. These wires are expected to accommodate large deflections while delivering low constant force. Clinically, this stage of treatment levels and aligns teeth via intrusion/extrusion, rotation, translation and tip. Rectangular cross sections are introduced in each case when torque is required to correct the malocclusion.
TABLE 1Exemplary Wire Sizes and GeometriesSize [inches]Geometry0.014Round0.016Round0.018Round0.016 × 0.016Square0.014 × 0.025Rectangular0.016 × 0.025Rectangular0.018 × 0.025Rectangular0.019 × 0.025Rectangular0.021 × 0.025Rectangular
For example, upon greater than 2% strain either in tensile or flexure (deflection), typical 0.016″ round nickel titanium wires express ˜300 MPa loading and ˜200 MPa unloading on a standard stress strain curve. This hysteresis may be problematic because there is likely to be a discrepancy of force between clinician installation and wire operation. In addition, the greater hysteresis for SMA's represents a greater likelihood of fatigue. Further, mastication introduces cycling thru the loading and unloading stress plateaus on the material, growing the hysteresis and effectively reducing the biological correction forces. Finally, larger strains introduce greater hysteresis for traditional nickel titanium alloys, thus greater malocclusions are difficult to treat and often introduce permanent sets.
Thus, it would be beneficial to manufacture archwires that address these problems, yet still exhibit some of the beneficial properties of nickel titanium alloys. Described herein are archwires made of “hyperelastic” (rather than simply superelastic) shape memory alloys that may address many of the problems mentioned above.
As described in detail below, hyperelastic SMA exhibit properties enabling them to undergo large recoverable distortions. Such distortions can be at least an order of magnitude greater than that which could be obtained if the component were made of non-SMA metals and alloys, and nearly an order of magnitude greater than can be obtained with polycrystalline SMA materials.
Examples of hyperelastic SMA include single crystal copper-based shape memory alloys including: CuAlNi, CuNiMn, and CuAlBe. See, e.g., WO2005/108635, filed Nov. 17, 2005, and U.S. Pat. No. 7,842,143. Hyperelastic wires may have a fully recoverable strain exceeding 10 percent; a very small thermomechanical hysteresis; phase transition temperatures ranging from cryogenic to more than 200° C.; low stress-induced-martensite stresses; and low effective sliding friction. These alloys are also biocompatible (see, e.g., Johnson, “Biocompatibility of copper-based single crystal shape memory alloys,” Proceedings of the International Conference on Shape Memory and Superelastic Technologies, Shuichi Miyazaki editor, SMST-2007, Tskuba, Japan, December 2007, and US 2009/0187243).
In addition to CuAlNi, CuAlMn and CuAlBe, other alloys are known to be hyperelastic and may be used as described herein. Compositions range from: CuAl(14-14.5)Ni(3-4.5) with CuAl(14.3)Ni(4.5) preferred for dental arches; CuAl(12)Be(0.5); and CuAl(11.5-12.8)Mn(4.5-8) weight percent. Others are being investigated, such as CuAl(12)Ni(4)Mn(2)Ti(1).
Specifically, hyperelastic single crystal SMAs have many advantages over polycrystal SMAs. For example, single crystal SMAs may exhibit greater than 10 percent strain recovery; there is a large gain in performance over the conventional SMA materials made from bulk materials, such as NiTi. Single crystal SMAs may also exhibit true constant force deflection. Unlike polycrystalline materials which reach their strain/stress plateau strength in a gradual fashion and maintain an upward slope when deformed further, hyperelastic SMA materials have a very sharp and clear plateau strain/stress that provides a truly constant stress when deformed up to 10 percent. The stress level at which the plateau occurs depends on the temperature difference between the transformation temperature and the loading temperature. Additionally, some single crystal SMAs exhibiting hyperelasticity, for example CuAlBe, benefit from a second stress plateau which can increase the total recoverable strain to 22 percent.
Single crystal SMAs may also have a very narrow loading-unloading hysteresis. As a result there is substantially the same constant force during both loading (increasing stress) and unloading (decreasing stress). This characteristic may be important for applications where the flexure undergoes repeated cycling, as with archwires.
Further, single crystal SMAs may exhibit recovery which is 100 percent repeatable and complete. One of the drawbacks of polycrystalline SMA materials has always been the “settling” that occurs as the material is cycled back and forth. The settling problem has required that the material be either “trained” as part of the manufacturing process, or designed into the application such that the permanent deformation which occurs over the first several cycles does not adversely affect the function of the device. By comparison, hyperelastic SMA materials do not develop such permanent deformations and therefore significantly simplify the design process into various applications.
Copper-based hyperelastic single crystal SMAs exhibit generally lower stress levels than titanium-based alloys. In fact, because the stress-induced martensite transformation is complete, the stress plateau can be near zero or as large as several hundred megapascals depending on composition and temperature. This adjustable nature of hyperelastic SMAs allows greater versatility in clinical applications.
Unlike NiTi SMAs, which must be conditioned, through a combination of alloying, heat treatment and cold working, to have superelastic properties, single crystal CuAlNi SMA has intrinsic hyperelastic properties: a crystal of CuAlNi may be hyperelastic immediately after being formed as described herein, with no further processing required.
Although single crystal SMAs have been known for several years, to date they have not been successfully used to create archwires, at least in part because it has proven difficult to shape such hyperelastic materials into the archwire form without destroying the single crystal properties by introducing dislocations in the crystal structure. In particular, known fabrication techniques for polycrystalline SMAs and even known methods of fabricating single crystal SMAs are inadequate when forming archwires, particularly those having non-circular cross-sections and/or those pre-bent in the arch shape.